On the advancements of conformal transformations and their associated symmetries in geometry and theoretical physics

Kastrup, H.A.

doi:10.1002/andp.200810324

Cited by 87 publications

(114 citation statements)

References 188 publications

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“…Mercator projection) to electromagnetism (see e.g. the work of Bateman [1]) to quantum theories [2]. In relativity and cosmology conformal transformations are also widely used.…”

Section: Introductionmentioning

confidence: 99%

Conformal transformations in cosmology of modified gravity: the covariant approach perspective

2010

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The 1+3 covariant approach and the covariant gauge-invariant approach to perturbations are used to analyze in depth conformal transformations in cosmology. Such techniques allow us to obtain insights on the physical meaning of these transformations when applied to non-standard gravity. The results obtained lead to a number of general conclusions on the change of some key quantities describing any two conformally related cosmological models. For example, even if some of the geometrical properties of the cosmology are preserved (homogeneous and isotropic Universes are mapped into homogeneous and isotropic universes), it can happen that decelerating cosmologies can be mapped into accelerated ones. From the point of view of the cosmological perturbations it is shown how these fluctuation transform. We find that first-order vector and tensor perturbations equations are left unchanged in their structure by the conformal transformation, but this cannot be said of the scalar perturbations, which present differences in their evolutionary features. The results obtained are then explicitly interpreted and verified with the help of some clarifying examples based on f (R)-gravity cosmologies.

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“…Mercator projection) to electromagnetism (see e.g. the work of Bateman [1]) to quantum theories [2]. In relativity and cosmology conformal transformations are also widely used.…”

Section: Introductionmentioning

confidence: 99%

Conformal transformations in cosmology of modified gravity: the covariant approach perspective

2010

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“…Conformal transformations have been utilised in geometry and physics for more than a century [14]. The twistor program of Penrose [15] views space-time points as collections of null geodesics and obtains results concerning zero rest mass particles and fields.…”

Section: Advances In Mathematical Physicsmentioning

confidence: 99%

An Approach to Classical Quantum Field Theory Based on the Geometry of Locally Conformally Flat Space-Time

Mashford

2017

Advances in Mathematical Physics

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This paper gives an introduction to certain classical physical theories described in the context of locally Minkowskian causal structures (LMCSs). For simplicity of exposition we consider LMCSs which have locally Euclidean topology (i.e., are manifolds) and hence are Möbius structures. We describe natural principal bundle structures associated with Möbius structures. Fermion fields are associated with sections of vector bundles associated with the principal bundles while interaction fields (bosons) are associated with endomorphisms of the space of fermion fields. Classical quantum field theory (the Dirac equation and Maxwell's equations) is obtained by considering representations of the structure group ⊂ SU(2, 2) of a principal bundle associated with a given Möbius structure where , while being a subset of SU(2, 2), is also isomorphic to SL(2, C) × (1). The analysis requires the use of an intertwining operator between the action of on R 4 and the adjoint action of on su(2, 2) and it is shown that the Feynman slash operator, in the chiral representation for the Dirac gamma matrices, has this intertwining property.

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“…In addition, here we are interested in special conformal symmetry. Since, the special conformal transformation can be obtained through the series of operations: (inversion) (translation) (inversion), as discussed in [1,24], the inversion operation…”

Section: Massive and Massless Single Particle Snyder Modelmentioning

confidence: 99%

Conformal invariance in noncommutative geometry and mutually interacting Snyder particles

Pramanik

Ghosh

Pal³

2014

Phys. Rev. D

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A system of relativistic Snyder particles with mutual two-body interaction that lives in a Non-Commutative Snyder geometry is studied. The underlying novel symplectic structure is a coupled and extended version of (single particle) Snyder algebra. In a recent work by Casalbuoni and Gomis, Phys.Rev. D90, 026001 (2014) [1], a system of interacting conventional particles (in commutative spacetime) was studied with special emphasis on it's Conformal Invariance. Proceeding along the same lines [1] we have shown that our interacting Snyder particle model is also conformally invariant. Moreover, the conformal Killing vectors have been constructed. Our main emphasis is on the Hamiltonian analysis of the conformal symmetry generators. We demonstrate that the Lorentz algebra remains undeformed but validity of the full conformal algebra requires further restrictions.

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On the advancements of conformal transformations and their associated symmetries in geometry and theoretical physics

Cited by 87 publications

References 188 publications

Conformal transformations in cosmology of modified gravity: the covariant approach perspective

Conformal transformations in cosmology of modified gravity: the covariant approach perspective

An Approach to Classical Quantum Field Theory Based on the Geometry of Locally Conformally Flat Space-Time

Conformal invariance in noncommutative geometry and mutually interacting Snyder particles

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